Synergy and redundancy in the Granger causal analysis of dynamical networks

We analyze by means of Granger causality the effect of synergy and redundancy in the inference (from time series data) of the information flow between subsystems of a complex network. Whilst we show that fully conditioned Granger causality is not affected by synergy, the pairwise analysis fails to put in evidence synergetic effects. In cases when the number of samples is low, thus making the fully conditioned approach unfeasible, we show that partially conditioned Granger causality is an effective approach if the set of conditioning variables is properly chosen. We consider here two different strategies (based either on informational content for the candidate driver or on selecting the variables with highest pairwise influences) for partially conditioned Granger causality and show that depending on the data structure either one or the other might be valid. On the other hand, we observe that fully conditioned approaches do not work well in presence of redundancy, thus suggesting the strategy of separating the pairwise links in two subsets: those corresponding to indirect connections of the fully conditioned Granger causality (which should thus be excluded) and links that can be ascribed to redundancy effects and, together with the results from the fully connected approach, provide a better description of the causality pattern in presence of redundancy. We finally apply these methods to two different real datasets. First, analyzing electrophysiological data from an epileptic brain, we show that synergetic effects are dominant just before seizure occurrences. Second, our analysis applied to gene expression time series from HeLa culture shows that the underlying regulatory networks are characterized by both redundancy and synergy

Quantitative Analysis of the Effective Functional Structure in Yeast Glycolysis

Yeast glycolysis is considered the prototype of dissipative biochemical oscillators. In cellular conditions, under sinusoidal source of glucose, the activity of glycolytic enzymes can display either periodic, quasiperiodic or chaotic behavior. In order to quantify the functional connectivity for the glycolytic enzymes in dissipative conditions we have analyzed different catalytic patterns using the non-linear statistical tool of Transfer Entropy. The data were obtained by means of a yeast glycolytic model formed by three delay differential equations where the enzymatic speed functions of the irreversible stages have been explicitly considered. These enzymatic activity functions were previously modeled and tested experimentally by other different groups. In agreement with experimental conditions, the studied time series corresponded to a quasi-periodic route to chaos. The results of the analysis are three-fold: first, in addition to the classical topological structure characterized by the specific location of enzymes, substrates, products and feedback regulatory metabolites, an effective functional structure emerges in the modeled glycolytic system, which is dynamical and characterized by notable variations of the functional interactions. Second, the dynamical structure exhibits a metabolic invariant which constrains the functional attributes of the enzymes. Finally, in accordance with the classical biochemical studies, our numerical analysis reveals in a quantitative manner that the enzyme phosphofructokinase is the key-core of the metabolic system, behaving for all conditions as the main source of the effective causal flows in yeast glycolysis.Comment: Biologically improve

Analysis of some factors and COVID-19 mortality in the population of 0 to 24 years in 29 countries: open schools could be a protection

Background. It is limited literature on the possible factors related to mortality by COVID-19 in minors. Children and young people are generally considered vulnerable, especially in low-income countries, whereby consistent evidence must arise to protect them and avoid mortality. Methods. A multiple linear regression model was fit to evaluate the relationship between deaths per 100,000 inhabitants and pandemic containment policies, the duration of totally closed schools, and GDP in 29 countries under study. Results. Linear regression analysis shows that the association between deaths per 100k and the number of weeks of closed schools had a coef B=0.355, [CI 0.010; 0.699], and it is statistically significant (P-value =0.044). Similarly, the association between deaths per 100K and GDP was -0.001, [CI -0.003; 0.001], and is not statistically associated (P-value 0.633). Conclusions. This study suggests that open schools could be a protective space for COVID-19 mortality in the child and youth population and that each country should implement studies on the subject at the local level

Identification of redundant and synergetic circuits in triplets of electrophysiological data

Neural systems are comprised of interacting units, and relevant information regarding their function or malfunction can be inferred by analyzing the statistical dependencies between the activity of each unit. Whilst correlations and mutual information are commonly used to characterize these dependencies, our objective here is to extend interactions to triplets of variables to better detect and characterize dynamic information transfer. Our approach relies on the measure of interaction information (II). The sign of II provides information as to the extent to which the interaction of variables in triplets is redundant (R) or synergetic (S). Here, based on this approach, we calculated the R and S status for triplets of electrophysiological data recorded from drug-resistant patients with mesial temporal lobe epilepsy in order to study the spatial organization and dynamics of R and S close to the epileptogenic zone (the area responsible for seizure propagation). In terms of spatial organization, our results show that R matched the epileptogenic zone while S was distributed more in the surrounding area. In relation to dynamics, R made the largest contribution to high frequency bands (14-100Hz), whilst S was expressed more strongly at lower frequencies (1-7Hz). Thus, applying interaction information to such clinical data reveals new aspects of epileptogenic structure in terms of the nature (redundancy vs. synergy) and dynamics (fast vs. slow rhythms) of the interactions. We expect this methodology, robust and simple, can reveal new aspects beyond pair-interactions in networks of interacting units in other setups with multi-recording data sets (and thus, not necessarily in epilepsy, the pathology we have approached here).Comment: 31 pages, 6 figures, 3 supplementary figures. To appear in the Journal of Neural Engineering in its current for

Disruption of transfer entropy and inter-hemispheric brain functional connectivity in patients with disorder of consciousness

Severe traumatic brain injury can lead to disorders of consciousness (DOC) characterized by deficit in conscious awareness and cognitive impairment including coma, vegetative state, minimally consciousness, and lock-in syndrome. Of crucial importance is to find objective markers that can account for the large-scale disturbances of brain function to help the diagnosis and prognosis of DOC patients and eventually the prediction of the coma outcome. Following recent studies suggesting that the functional organization of brain networks can be altered in comatose patients, this work analyzes brain functional connectivity (FC) networks obtained from resting-state functional magnetic resonance imaging (rs-fMRI). Two approaches are used to estimate the FC: the Partial Correlation (PC) and the Transfer Entropy (TE). Both the PC and the TE show significant statistical differences between the group of patients and control subjects; in brief, the inter-hemispheric PC and the intra-hemispheric TE account for such differences. Overall, these results suggest two possible rs-fMRI markers useful to design new strategies for the management and neuropsychological rehabilitation of DOC patients.Comment: 25 pages; 4 figures; 3 tables; 1 supplementary figure; 4 supplementary tables; accepted for publication in Frontiers in Neuroinformatic

Information transfer of an Ising model on a brain network

We implement the Ising model on a structural connectivity matrix describing the brain at a coarse scale. Tuning the model temperature to its critical value, i.e. at the susceptibility peak, we find a maximal amount of total information transfer between the spin variables. At this point the amount of information that can be redistributed by some nodes reaches a limit and the net dynamics exhibits signature of the law of diminishing marginal returns, a fundamental principle connected to saturated levels of production. Our results extend the recent analysis of dynamical oscillators models on the connectome structure, taking into account lagged and directional influences, focusing only on the nodes that are more prone to became bottlenecks of information. The ratio between the outgoing and the incoming information at each node is related to the number of incoming links

Consensus clustering approach to group brain connectivity matrices

A novel approach rooted on the notion of consensus clustering, a strategy developed for community detection in complex networks, is proposed to cope with the heterogeneity that characterizes connectivity matrices in health and disease. The method can be summarized as follows: (i) define, for each node, a distance matrix for the set of subjects by comparing the connectivity pattern of that node in all pairs of subjects; (ii) cluster the distance matrix for each node; (iii) build the consensus network from the corresponding partitions; (iv) extract groups of subjects by finding the communities of the consensus network thus obtained. Differently from the previous implementations of consensus clustering, we thus propose to use the consensus strategy to combine the information arising from the connectivity patterns of each node. The proposed approach may be seen either as an exploratory technique or as an unsupervised pre-training step to help the subsequent construction of a supervised classifier. Applications on a toy model and two real data sets, show the effectiveness of the proposed methodology, which represents heterogeneity of a set of subjects in terms of a weighted network, the consensus matrix

Enhanced pre-frontal functional-structural networks to support postural control deficits after traumatic brain injury in a pediatric population

Traumatic brain injury (TBI) affects the structural connectivity, triggering the re-organization of structural-functional circuits in a manner that remains poorly understood. We focus here on brain networks re-organization in relation to postural control deficits after TBI. We enrolled young participants who had suffered moderate to severeTBI, comparing them to young typically developing control participants. In comparison to control participants, TBI patients (but not controls) recruited prefrontal regions to interact with two separated networks: 1) a subcortical network including part of the motor network, basal ganglia, cerebellum, hippocampus, amygdala, posterior cingulum and precuneus; and 2) a task-positive network, involving regions of the dorsal attention system together with the dorsolateral and ventrolateral prefrontal regions

Information flow between resting state networks

The resting brain dynamics self-organizes into a finite number of correlated patterns known as resting state networks (RSNs). It is well known that techniques like independent component analysis can separate the brain activity at rest to provide such RSNs, but the specific pattern of interaction between RSNs is not yet fully understood. To this aim, we propose here a novel method to compute the information flow (IF) between different RSNs from resting state magnetic resonance imaging. After haemodynamic response function blind deconvolution of all voxel signals, and under the hypothesis that RSNs define regions of interest, our method first uses principal component analysis to reduce dimensionality in each RSN to next compute IF (estimated here in terms of Transfer Entropy) between the different RSNs by systematically increasing k (the number of principal components used in the calculation). When k = 1, this method is equivalent to computing IF using the average of all voxel activities in each RSN. For k greater than one our method calculates the k-multivariate IF between the different RSNs. We find that the average IF among RSNs is dimension-dependent, increasing from k =1 (i.e., the average voxels activity) up to a maximum occurring at k =5 to finally decay to zero for k greater than 10. This suggests that a small number of components (close to 5) is sufficient to describe the IF pattern between RSNs. Our method - addressing differences in IF between RSNs for any generic data - can be used for group comparison in health or disease. To illustrate this, we have calculated the interRSNs IF in a dataset of Alzheimer's Disease (AD) to find that the most significant differences between AD and controls occurred for k =2, in addition to AD showing increased IF w.r.t. controls.Comment: 47 pages, 5 figures, 4 tables, 3 supplementary figures. Accepted for publication in Brain Connectivity in its current for